# the Hyperbolic space has constant sectional curvature $-1$, why is not contradict to the Hadamard Theorem?

the Hadamard Theorem says that any simply connected, complete Riemannian manifold of non-positive sectional curvature is diffeomorphic to $$R_{n}$$. I know this is a stupid question, but what am I missing here?

• Hyperbolic space is diffeomorphic to $\mathbb{R}^n$. – Max Oct 30 '18 at 15:53
• So that's how it is..I am learning differential geometry by myself, the textbook never mention that. Thanks. – knot Oct 30 '18 at 15:58